Advanced Search
Impact Factor: 5.8

Volume 17 Issue 3

Sep.  2000

Article Contents
Article >  ADVANCES IN ATMOSPHERIC SCIENCES  > 2000 >  17(3): 375-390

The Impact of Nonlinear Stability and Instability on the Validity of the Tangent Linear Model

  • 1.

    LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,Joint Center for Earth System Technology, University of Maryland， Baltimore County, Maryland, USA


doi: 10.1007/s00376-000-0030-9

  • The impact of nonlinear stability and instability on the validity of tangent linear model (TLM) is investigated by comparing its results with those produced by the nonlinear model (NLM) with the identical initial perturbations. The evolutions of different initial perturbations superposed on the nonlinearly stable and unstable basic flows are examined using the two-dimensional quasi-geostrophic models of double periodic-boundary condition and rigid boundary condition.The results indicate that the valid time period of TLM, during which TLM can be utilized to approxi-mate NLM with given accuracy, varies with the magnitudes of the perturbations and the nonlinear stability and instability of the basic flows. The larger the magnitude of the perturbation is, the shorter the valid time period. The more nonlinearly unstable the basic flow is, the shorter the valid time period of TLM. With the double-periodic condition the valid period of the TLM is shorter than that with the rigid-boundary condi-tion.
  • [1] Xiang Jie, Sun Litan, 2002: Nonlinear Saturation of Baroclinic Instability in the Phillips Model: The Case of Energy, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 1079-1090.  doi: 10.1007/s00376-002-0066-0
    [2] Liu Yongming, Mu Mu, 1994: Arnol’d’s Second Nonlinear Stability Theorem for General Multilayer Quasi-geostrophic Model, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 36-42.  doi: 10.1007/BF02656991
    [3] LU Weisong, SHAO Haiyan, 2003: Generalized Nonlinear Subcritical Symmetric Instability, ADVANCES IN ATMOSPHERIC SCIENCES, 20, 623-630.  doi: 10.1007/BF02915505
    [4] Yong. L. McHall, 1992: Nonlinear Planetary Wave Instability and Blocking, ADVANCES IN ATMOSPHERIC SCIENCES, 9, 173-190.  doi: 10.1007/BF02657508
    [5] Lin Wantao, Ji Zhongzhen, Wang Bin, 2002: A Comparative Analysis of Computational Stability for Linear and Non-Linear Evolution Equations, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 699-704.  doi: 10.1007/s00376-002-0009-9
    [6] He Jianzhong, 1994: Nonlinear Ultra-Long Wave and Its Stability, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 91-100.  doi: 10.1007/BF02656998
    [7] Ji Zhongzhen, Lin Wantao, Yang Xiaozhong, 2001: Problems of Nonlinear Computational Instability in Evolution Equations, ADVANCES IN ATMOSPHERIC SCIENCES, 18, 397-403.  doi: 10.1007/BF02919318
    [8] Shen Xinyong, Ni Yunqi, Ding Yihui, 2002: On Problem of Nonlinear Symmetric Instability in Zonal Shear Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 350-364.  doi: 10.1007/s00376-002-0027-7
    [9] Li Yang, Mu Mu, Wu Yonghui, 2000: A Study on the Nonlinear Stability of Fronts in the Ocean on a Sloping Continental Shelf, ADVANCES IN ATMOSPHERIC SCIENCES, 17, 275-284.  doi: 10.1007/s00376-000-0009-6
    [10] Lin Wantao, Ji Zhongzhen, Wang Bin, 2001: Computational Stability of the Explicit Difference Schemes of the Forced Dissipative Nonlinear Evolution Equations, ADVANCES IN ATMOSPHERIC SCIENCES, 18, 413-417.  doi: 10.1007/BF02919320
    [11] JIANG Zhina, 2006: Applications of Conditional Nonlinear Optimal Perturbation to the Study of the Stability and Sensitivity of the Jovian Atmosphere, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 775-783.  doi: 10.1007/s00376-006-0775-x
    [12] Mu Mu, Zeng Qingcun, 1991: Criteria for the Nonlinear Stability of Three-Dimensional Quasi-Geostrophic Motions, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 1-10.  doi: 10.1007/BF02657360
    [13] LIU Yongming, CAI Jingjing, 2006: On Nonlinear Stability Theorems of 3D Quasi-geostrophic Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 809-814.  doi: 10.1007/s00376-006-0809-4
    [14] Li Yang, Mu Mu, 1996: On the Nonlinear Stability of Three-Dimensional Quasigeostrophic Motions in Spherical Geometry, ADVANCES IN ATMOSPHERIC SCIENCES, 13, 203-216.  doi: 10.1007/BF02656863
    [15] Liu Yongming, 1999: Nonlinear Stability of Zonally Symmetric Quasi-geostrophic Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 16, 107-118.  doi: 10.1007/s00376-999-0007-2
    [16] Mu Mu, Wu Yonghui, Tang Mozhi, Liu Haiyan, 1999: Nonlinear Stability Analysis of the Zonal Flows at Middle and High Latitudes, ADVANCES IN ATMOSPHERIC SCIENCES, 16, 569-580.  doi: 10.1007/s00376-999-0032-1
    [17] Zhu Jiang, Wang Hui, Masafumi Kamachi, 2002: The Improvement Made by a Modified TLM in 4DVAR with a Geophysical Boundary Layer Model, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 563-582.  doi: 10.1007/s00376-002-0001-4
    [18] Ren Shuzhan, 1991: Nonlinear Stability of Plane Rotating Shear Flow under Three-Dimensional Nondivergence Disturbances, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 129-136.  doi: 10.1007/BF02658089
    [19] Liu Yongming, Mu Mu, 1992: A Problem Related to Nonlinear Stability Criteria for Multi-layer Quasi-geostrophic Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 9, 337-345.  doi: 10.1007/BF02656943
    [20] Liu Shida, Liu Shikuo, 1985: NONLINEAR WAVES IN BAROTROPIC MODEL, ADVANCES IN ATMOSPHERIC SCIENCES, 2, 147-157.  doi: 10.1007/BF03179747
PDF

Get Citation+

shu
Export:  

Share Article

Article Metrics

Article Views: 1520 Times

PDF downloads: 1233 Times

Cited by: Times
  • 加载中

    • Manuscript History

    Manuscript received: 10 September 2000
    Manuscript revised: 10 September 2000
    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    The Impact of Nonlinear Stability and Instability on the Validity of the Tangent Linear Model

    • 1. LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,Joint Center for Earth System Technology, University of Maryland， Baltimore County, Maryland, USA
    • Manuscript received: 2000-09-10
    • Manuscript revised: 2000-09-10

    Abstract: The impact of nonlinear stability and instability on the validity of tangent linear model (TLM) is investigated by comparing its results with those produced by the nonlinear model (NLM) with the identical initial perturbations. The evolutions of different initial perturbations superposed on the nonlinearly stable and unstable basic flows are examined using the two-dimensional quasi-geostrophic models of double periodic-boundary condition and rigid boundary condition.The results indicate that the valid time period of TLM, during which TLM can be utilized to approxi-mate NLM with given accuracy, varies with the magnitudes of the perturbations and the nonlinear stability and instability of the basic flows. The larger the magnitude of the perturbation is, the shorter the valid time period. The more nonlinearly unstable the basic flow is, the shorter the valid time period of TLM. With the double-periodic condition the valid period of the TLM is shorter than that with the rigid-boundary condi-tion.

      HTML

    Catalog

      Publish with AAS

      Contact us

      Links

      Copyright © 2018-2028 ADVANCES IN ATMOSPHERIC SCIENCES 京ICP备14024088号-7

      Supported by: Beijing Renhe Information Technology Co. Ltd  support: info@rhhz.net  

      /

      DownLoad:  Full-Size Img  PowerPoint
      Return
      Return